In the past many different forms of light fixtures have been proposed, made and sold for providing two levels of illumination, a first level of illumination being utilized when it was desired to have a high light level, and a second level of illumination being utilized when a lower level of light was desired, such as at night. The light fixtures that have been proposed heretofore to provide this function have had several problems and deficiencies. One of the more annoying problems has been that such fixtures were physically constructed in a manner such that it was very difficult to remove and replace one or both of the light bulbs, when desired. Another problem with the prior devices is that the mounting structures for the light bulbs were constructed in a manner such that the resulting light fixtures were unduly complicated and expensive to fabricate.